Possession letter from builder

The builder handed over possession to the original owner hence he would deliver the possession letter on his name only.

There's no legal infirmity in it.

In any case this is just an additional document to you and not a title document, hence you may not dispute the same even if it is on the name of the first owner.

In the given facts, the possession letter is hardly of any significance as to your title to the property.

The first owner, while executing the sale deed, shall mention the possession certificate details in the document provided to you (the purchaser). A title deed is important.

Whether the builder had handed over physical possession to the vendor (seller) of the subject property before you purchased it ? If so, possession letter is formal and insignificant. 

Since the builder neither had  executed. sale deed in favour of you nor handoverd possession of property to you so how can he issue possession letter to you, he can issue the possession letter 0nly  to whom he has handoverd possession of property and execute sale deed.

Dear Sir,

Is it appropriate if the builder issues the possession letter in the name of the previous owner, and we sign and acknowledge it on behalf of [Name of Previous Owner], since the previous owner resides in another state and cannot come personally?

If the builder is ready and willing to accept your acknowledgment for the receipt of this possession letter then you can inform the previous owner and get his consent over whatsapp or even orally over phone and then collect it from the builder. 

You have purchased the property from some person other than the Builder, without transfer and replacement of names in the  records of builder, isn't it ? If so, you are an outsider and alien for the builder. 

It will be appropriate to consult a local prudent lawyer with relevant records for proper appreciation of facts / documents,  professional advise and necessary proceeding.